Answer
$pH = 1.89$
Work Step by Step
1. Find the concentrations of $HCl$ and $HI$ after the dilution:
Total volume : $50ml + 125ml = 175ml$
$HCl:$
$C_i * V_i = C_f * V_f$
$0.020 * 0.050 = C_f * 0.175$
$0.001 = C_f * 0.175$
$C_f = 5.71 \times 10^{-3}M$
$HI:$
$C_i * V_i = C_f * V_f$
$0.01 * 0.125 = C_f * 0.175$
$0.00125 = C_f * 0.175$
$C_f = 7.14 \times 10^{-3}M$
2. Since they are strong acids:
$[HCl] +[HI] = [H^+]$
$5.71 \times 10^{-3} + 7.14 \times 10^{-3} = [H^+]$
$[H^+] = 1.285 \times 10^{-2}M$
3. Calculate the pH:
$pH = -log[H^+]$
$pH = -log(1.285 \times 10^{-2})$
$pH = 1.89$
